The behavior of many systems of practical interest in communications and other areas is well
modeled by a single server exponential queueing system in which the arrival and service rates are
dependent upon the state of a Markov chain, the dynamics of which are independent of the queue
length. Formal solution to such models based on Neuts's matrix geometric approach have appeared
frequently in the literature. A major problem in using the matrix geometric approach is the computation
of the rate matrix, which requires the solution of a matrix polynomial. In particular,
computational times appear to be unpredictable and excessive for many problems of practical interest.
Alternative techniques which employ eigenanalysis have been developed. These techniques are
polynomially bounded and yield results very quickly compared to iterative routines. On the other
hand, the class of systems to which the eigenanalysis based techniques apply have been somewhat
restricted. In this thesis, we modify the eigenanalysis approach initially presented in order to remove
some of these restrictions.
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